Answer Set Programming Based on Propositional Satisfiability

Abstract

Abstract. Answer Set Programming (ASP) emerged in the late 1990s as a new logic programming paradigm which has been successfully applied in various application domains. Also motivated by the availability of efficient solvers for propositional satisfiability (SAT), various reductions from logic programs to SAT were introduced in the past. All these reductions either are limited to a subclass of logic programs, or introduce new variables, or may produce exponentially bigger propositional formulas.In this paper, we present a SAT-based procedure, called ASP-SAT, that (i) deals with any (non disjunctive) logic program, (ii) works on a propositional formula without additional variables (except for those possibly introduced by the clause form transformation), and (iii) is guaranteed to work in polynomial space. From a theoretical perspective, we prove soundness and completeness of ASP-SAT. From a practical perspective, we have (i) implemented ASP-SAT in Cmodels, (ii) extended the basic procedures in order to incorporate the most popular SAT reasoning strategies, and (iii) conducted an extensive comparative analysis involving also other state-of-the-art answer set solvers. The experimental analysis shows that our solver is competitive with the other solvers we considered, and that the reasoning strategies that work best on "small but hard" problems are ineffective on "big but easy" problems and vice versa.

On the relation among answer set solvers

“…ASP solvers could benefit (at least on tight programs) from the great amount of work done in SAT: search strategies, heuristics and combinations, which have been shown to be effective in SAT, can be imported (with the necessary adaptations) in ASP systems leading to similar improvements. This is indeed the case as shown in [24,27] (where results are shown to experimentally extend to nontight programs), and this is the current research trend that the main groups working on native procedures are following, by implementing optimized look-back techniques and heuristics in order to more efficiently handling "real-world" problems (see, e.g., [20,40,48] 7 ).…”

“…3.1 cmodels cmodels [27] is a SAT-based ASP system which reduces the problem of answer set computation to the satisfiability problem of propositional formulas via Clark's completion, and uses a SAT solver as search engine. In order for the formula to be fed to a SAT solver, it needs to be converted into Conjunctive Normal Form (CNF), usually by adding variables (denoted with the set N).…”

“…Here we consider the one proposed in [27] (called ASP-SAT in that paper) without learning, which also corresponds to the description on the cmodels's home page, and it is represented in Fig. 1, where -is the input program; is a set of clauses; I is an interpretation; p and l are an atom and a literal, respectively.…”

“…Programs corresponding to random k-CNF formulas have been widely used in literature, e.g., in [15,27,50,54].…”

“…In particular, on the class of tight programs SAT-based systems are very efficient, often more efficient than native solvers, see, e.g., [27,38] and the results of the First Answer Set Programming competition.…”